Abstract
In this chapter we study modular spaces and Musielak–Orlicz spaces which provide the framework for a variety of different function spaces, including classical (weighted) Lebesgue and Orlicz spaces and variable exponent Lebesgue spaces. Although our aim mainly is to study the latter, it is important to see the connections between all of these spaces. Many of the results in this chapter can be found in a similar form in [295], but we include them to make this exposition self-contained. Research in the field of Musielak–Orlicz functions is still active and we refer to [67] for newer results and references.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Diening, L., Harjulehto, P., Hästö, P., Růžička, M. (2011). A Framework for Function Spaces. In: Lebesgue and Sobolev Spaces with Variable Exponents. Lecture Notes in Mathematics(), vol 2017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18363-8_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-18363-8_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-18362-1
Online ISBN: 978-3-642-18363-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)